## 24. Second, we apply these estimates to back-cast subsidy values over 2009-23.

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---

### Relationship between subsidy values and counts
- Empirical specification: ∆S^j_{i,t} = f(∆NS^j_{i,t}) + α_i + μ_j + δ_t + ε^j_{i,t}, where:
  - i = country, t = year (2023 and 2024), j = sector (OECD ICIO).
  - α captures country fixed effects; μ industry fixed effects; δ a year dummy.
- Focus and data:
  - Focus on goods sectors; aggregate service industry assigned a subsidy of zero in model simulations.
  - Data source for counts: GTA (changes in subsidy counts); data for values: NIPO (used to estimate f(·)).
- Estimated predictive coefficients:
  - Selected predictive coefficient (linear specification): 35.8 on ∆NS (standard error = 9.5).
  - Alternative estimate when excluding fixed effects: coefficient = 47.3 (standard error = 12.7) — scales up estimated subsidy value uniformly across countries and sectors.

### Cross-validation and model selection
- Procedure:
  - 10-fold cross-validation (folds formed by randomly selecting groups of countries; 39 plus the EU per fold).
  - Candidate functions for f(·): dummy variables for up to 20 quantiles of ∆NS, linear, and polynomial functions up to fifth order.
  - Performance metric: median absolute deviation (MAD) of prediction errors.
- Result:
  - Linear model minimizes both median and average MAD and is selected.

### Data cleaning and alignment with the model
- Instrument inclusion/exclusion:
  - Restrict to subsidy measures transferring resources directly from governments to firms.
  - Included NIPO categories: “Production subsidies”, “State aid, unspecified", “Capital injection and equity stakes (including bailouts)", “Financial grant", “In-kind grant", and “State aid, nes" (grouping follows UNCTAD(2019) classification).
  - Excluded measures: tax breaks and preferential state loans.
- Budgeted vs. disbursed amounts:
  - Allocate budgeted value proportionally over subsidy duration based on days active within each year.
  - Example: subsidy introduced July 1, 2023 and expiring June 30, 2024 → budget split equally between 2023 and 2024.
  - For measures without specified expiration date (about 80 percent of the sample), impute duration using sample average of about 809 days.
- Product targeting and sector mapping:
  - NIPO specifies HS 6-digit products (2012 revision); to construct subsidy rates for 24 OECD ICIO sectors, aggregate values and counts within each sector and allocate measures spanning multiple sectors proportionally based on sectoral share of targeted HS 6-digit products.
- Note:
  - Restricting to direct transfers understates total subsidy support over time because tax reductions and preferential credit have become more important.

### Back-casting methodology and sample construction
- Application of estimated relationship:
  - Apply NIPO-estimated linear relationship (coefficient = 35.8 on ∆NS) to full NIPO dataset and to yearly changes in subsidy counts from GTA to predict annual changes in subsidy values from 2009 onward.
- GTA processing:
  - Within GTA: calculate cumulative sum of subsidy measures introduced since 2009 that remain in force in each given year up to 2023.
  - Apply same cleaning steps to GTA as for NIPO: restrict to direct transfers, impute durations for measures without expiration dates, distribute multi-sector subsidies proportionally.
  - For each sector, count variable equals difference between GTA-classified trade-distortive (“red”) subsidy measures and the (very low) number of trade-liberalizing (“green”) subsidies.
- Analysis period and sample restriction:
  - Focus period for analysis and simulations: start in 2015 to reduce downward bias from missing legacy subsidies introduced before 2009 and because industrial policy activity increased after 2015.
  - Sample restriction for simulations: 10 largest subsidizers during 2015-23; other countries grouped as rest-of-the-world (ROW).
- Units and extensions:
  - Predicted subsidy values expressed as share of sectoral value added from OECD ICIO tables.
  - OECD ICIO extends through 2022; for 2023 sectoral value added estimated by applying country-level annual GDP growth rates to 2022 sectoral values.

### Estimated subsidy patterns and strategic sectors
- Countries in model simulations: ten largest subsidizers (per 2015-23 estimates) plus ROW.
- Country-level and aggregate measures (2015-23):
  - China:
    - Average subsidy relative to value added over 2015-23 = 1.8 percent.
    - Subsidies grew from 1 to 2.6 percent of value added over the period.
  - United States:
    - Aggregate subsidy rate = 1.3 percent over 2015-23.
  - European Union:
    - Aggregate subsidy rate = 0.6 percent over 2015-23.
    - Estimated direct subsidies as share of goods value added in 2023 = 1 percent (comparison point cited).
- Global averages in 2023:
  - Strategic sectors: 1.8 percent of value added.
  - Other sectors: 0.9 percent of value added.
  - In 2015 both strategic and other sectors = 0.5 percent.
- Definition of strategic sectors:
  - Use Advanced Technology Products (ATPs) list from US Census Bureau: 518 HS 10-digit products (HS 2012), grouped into ten categories (biotechnology, life sciences, opto-electronics, information & communications, electronics, flexible manufacturing, advanced materials, aerospace, weapons, and nuclear technology).
  - Match ATP list to GTA product-level data, aggregate to HS 6-digit (consider HS 6-digit an ATP if at least one HS 10-digit subcategory is ATP).
  - OECD ICIO sectors containing at least one ATP (eight sectors designated strategic): fabricated metals, other manufacturing, chemicals, pharmaceuticals, electrical equipment, machinery, transport equipment, and electronics.
- Observed allocation and trends:
  - Subsidies directed more toward strategic sectors in most countries; largest differences in China, Canada and Russia.
  - In US and EU, subsidies as share of value added higher in non-strategic sectors.
  - Increased bias toward strategic sectors over 2015-23, with largest increases in China, Australia, India and Canada.
  - Country-level total subsidies over gross output in goods sectors during 2015-23: China = 0.5 percent, US = 0.5 percent, EU = 0.2 percent.
- Sectoral detail:
  - China: largest subsidy rate increases in pharmaceuticals, electronics, and electrical equipment — all strategic.
  - US and EU: large increases observed in non-strategic sectors like agriculture and mineral products.
  - Australia and Canada: largest increases in subsidy rates affecting strategic sectors (electronics and electrical equipment), starting from values close to zero in 2015.

### Comparisons with other measurement initiatives
- MAGIC database (OECD,2025a) and other sources:
  - MAGIC reported China’s average subsidy rate from grants as percentage of total revenues in sampled firms = 0.5 percent over 2005-22, matching the paper’s average during 2015-23.
  - OECD (2025a) reports North America average over 2005-22 for grants as percent of revenues = 0.1 percent; paper’s US 2015-23 average estimated subsidy as percent of gross output = 0.5.
  - European Commission State Aid Scoreboard (European Commission,2025) reports 0.6 percent of GDP (including services); paper reports 1 percent of goods value added in 2023.

### Data caveats and limitations
- Under-counting and missing legacy measures:
  - GTA likely under-counts policy measures in smaller and emerging economies; excluding years before 2015 mitigates but does not eliminate under-counting (example: zero subsidy counts for Saudi Arabia and Argentina in early years of 2015-23).
  - Legacy subsidies introduced before 2009 but active during 2015-23 are missing and bias estimates downward.
- Measurement and comparability issues:
  - Cross-country comparisons complicated by reliance on mixed sources that can record firm- or region-specific measures separately when they belong to a single policy intervention.
  - Estimation hinges on empirical relationship between subsidy values and counts estimated on NIPO data as of February 2025; future data releases may shift this relationship and affect back-casting.
  - Restricting to direct transfer instruments likely understates overall subsidy values because tax reductions and preferential credit are increasingly important.
  - Underestimation of subsidy values for emerging economies may be substantial; alternative evidence suggests “direct funding” can account for around 1.5 percent of GDP in middle income economies (Fernandes and Reed (2026) — noted as context).

---

### 4.1 Trade effects of subsidies

### Model framework and calibration highlights
- Model structure:
  - Multi-country multi-sector general equilibrium model with N countries and J sectors; workers immobile across countries but mobile across sectors within a country.
  - Representative consumer: Cobb-Douglas across sectors and CES across varieties.
  - Country i can apply a uniform production subsidy s^j_i across destinations; define ˜t^j_in ≡ 1 + t^j_in and ˜s^j_i ≡ 1 + s^j_i.
  - Productivity z^j_i(ω) drawn i.i.d. from a Fréchet distribution; scale elasticities ψ^j capture external scale economies.
- Equilibrium and gravity relations:
  - Sectoral price index: P^j_n = [∑_{i=1}^N T^j_i (c^j_i τ^j_in ˜t^j_in ˜s^j_i)^{−θ^j}]^{−1/θ^j}.
  - Expenditure share: π^j_in = T^j_i (˜s^j_i)^{θ^j} (c^j_i τ^j_in ˜t^j_in)^{−θ^j} (P^j_n)^{−θ^j}.
- Calibration targets and baseline:
  - Ten countries with largest estimated subsidies during 2015-23 and ROW aggregate.
  - 20 sectors: 19 goods sectors plus a services aggregate.
  - Base year for trade flows: OECD ICIO database for 2015.
  - Subsidy shocks calibrated using 2015-23 estimates divided by sectoral gross output kept fixed at its 2015 level.
  - Baseline assumes import tariffs and bilateral trade costs held constant: ˆτ^j_in = ˆ˜t^j_in = 1.
- Key parameter ranges used:
  - Sectoral trade elasticities θ^j for manufacturing: range from 2.9 to 8.9.
  - Scale elasticities ψ^j: range from 0.06 to 0.22; set to zero for non-manufacturing sectors.

### Trade effects: mechanism and quantitative outcomes
- Mechanism:
  - Subsidies reallocate resources toward targeted industries and away from others, raising production and exports in more heavily subsidized sectors and reducing imports in those sectors.
  - Economies of scale amplify effects: higher ψ^j yields larger productivity surges and export responses.
  - Multiple channels operate: direct price effects (θ^j ∆ ln ˜s^j_i), productivity (θ^j ψ^j ∆ ln L^j_i), wage effects, input-price effects, competition and importer-expenditure channels.
- Country-specific simulated impacts (2015-23 subsidy changes):
  - China-only scenario:
    - Exports in strategic sectors rise by 12 percent.
    - Imports in strategic sectors drop by 8 percent.
    - China’s trade surplus in strategic sectors is 30 percent higher at 0.7 trillion USD in the counterfactual than at baseline.
  - EU and US scenarios:
    - Subsidies increase exports and decrease imports in strategic sectors; effects smaller than China’s.
  - All ten largest subsidizers and ROW implementing 2015-23 changes:
    - Trade effects qualitatively similar to China-only scenario; China’s role remains dominant.
- Cross-border spillovers:
  - EU and US exports in strategic sectors decline by around 2 percent following China-only subsidies.
  - ROW aggregate experiences largest percent contraction in exports in strategic sectors under China-only subsidies.
  - Non-subsidizing countries increase their imports by up to 3 percent.
  - Exceptions: Australia and Canada register large percent increases in exports in strategic sectors under all-subsidizer scenario.
- Global market shares and sectoral balances:
  - China’s share of world exports in strategic sectors rises from 27 percent at baseline to 29 percent under the subsidy counterfactual.
  - China’s net electronics exports surge from 0.2 trillion to approximately 0.3 trillion USD.
  - Policy shocks leave aggregate trade balances unchanged by construction but shift sectoral net exports substantially.
- Sectoral detail — Electronics:
  - China’s electronics exports increase by around 20 percent.
  - China’s share of world electronics exports increases from 39 to 45 percent.
  - Resources shift away from less-subsidized baseline sectors such as textiles and agriculture.
  - Under all-subsidizer scenario, EU and US experience substantial reductions in electronics exports; Australia, Canada, and India see largest percent increases.

### Role of economies of scale and robustness
- No-scale counterfactual (ψ^j = 0):
  - Trade effects are weaker: China’s exports in strategic sectors increase by 5 percent (compared with 12 percent in baseline).
  - Indicates up to half of China’s export response attributable to induced productivity changes.
- Alternative scale elasticities:
  - Higher ψ^j (Bartelme et al. baseline without input-output linkages): China’s exports in strategic sectors increase by more than 40 percent; other countries’ exports fall by more than 10 percent in those industries.
  - Results qualitatively robust across alternative elasticity calibrations (Lashkaripour and Lugovskyy (2023)).

### Interaction with recent tariff actions (2015–March 2026)
- Tariff chronology and magnitudes (import-weighted averages, 2015 → subsequent years):
  - US average tariffs on imports from China: 3 percent in 2015 → 16 percent after 2018-19 → 31 percent as of March 2026.
  - China’s average tariffs on US imports: 6 percent in 2015 → 27 percent as of March 2026.
  - In China, non-strategic sectors’ import-weighted tariffs on US imports: 8 percent → 34 percent; strategic sectors: 4 percent → 22 percent.
  - US tariffs on all trading partners: increased to 16.4 percent as of March 2026 (strategic sectors reached 16.4 percent), surpassing other sectors at 13.7 percent.
- Interaction outcomes:
  - US-China 2018-19 tariffs lower China’s export growth in strategic sectors and deepen China’s import drop relative to subsidy-only scenario.
  - Under subsidy-only scenario, China’s exports to the US in strategic sectors increase by 12 percent; with 2018-19 tariffs included that 12 percent increase reverses to a 30 percent decline.
  - 2025 tariff actions compound effects: under subsidies + tariffs as of March 2026:
    - China’s exports in strategic sectors decline by 4 percent.
    - US imports in strategic and other sectors plummet by around 25 percent; US exports drop relatively less.
    - In the US, domestic sales in strategic sectors increase by around 13 percent.
  - Tariffs attenuate trade deflection and reduce economies-of-scale-driven expansions.

### Efficiency and welfare implications
- General findings:
  - In models with economies of scale, subsidies and import tariffs have ambiguous effects on efficiency and welfare.
  - Production subsidies proportional to sectoral scale elasticities are first best; observed subsidy distributions deviate from this and create misallocation.
- Simulated welfare outcomes:
  - Welfare decreases globally under the subsidies scenario as fiscal costs outweigh any efficiency gains.
  - Real wages go up in most countries under the 2015-23 subsidy changes because changes in subsidy rates correlate with scale elasticities.
  - Despite higher real wages, real income (welfare-relevant, includes changes in net government expenditure) decreases globally and for most countries under the subsidies scenarios.
  - Adding recent tariff actions deepens global inefficiencies and creates asymmetric effects:
    - Counterfactual losses in global welfare widen when tariffs are added.
    - US welfare increases slightly under the 2025 tariff scenario because higher tariff revenues more than offset the reduction in real wages (conditional on limited retaliation).
    - Welfare losses deepen for all tariffed countries under the subsidy-and-tariff scenario.
- Robustness:
  - Without external economies of scale, subsidies reduce welfare for all countries; tariffs are welfare reducing also for the US in that variant.
  - Higher scale elasticities amplify efficiency gains for large subsidizers (e.g., China, Canada) but global welfare remains reduced once fiscal costs and tariff externalities are included.

### Conclusion and suggested future research avenues
- Key conclusions:
  - China’s subsidies in strategic sectors, especially electronics, have notable trade impacts through productivity responses.
  - Subsidies by the EU, the US, and other major subsidizers exert relatively smaller trade spillovers.
  - Subsidies during 2015-23 are higher in sectors with stronger production externalities, increasing real wages, but fiscal costs and terms-of-trade effects outweigh efficiency gains.
  - Tariffs deepen efficiency losses; a subsidy-tariff spiral amplifies global inefficiencies.
- Future research directions suggested:
  - Explore the role of other industrial policy instruments, such as tax incentives and preferential financing.
  - Incorporate dynamic elements and frictions to capture adjustment costs and transitions to long-run changes.
  - Improve calibration and understanding of scale elasticities, especially for non-manufacturing sectors and services.
  - Model endogenous policy responses by trade partners to better capture interactive adjustments to changing trade flows.

*Source: wpiea2026155-source-pdf - 24. Second, we apply these estimates to back-cast subsidy values over 2009-23.; IMF working paper chapter "4.1 Trade effects of subsidies" (wpiea2026155-source-pdf).*

### 24. Second, we apply these estimates to back-cast subsidy values over 2009-23.

### 24. Second, we apply these estimates to back-cast subsidy values over 2009-23.

### Relationship between subsidy values and counts
- Empirical specification: ∆S^j_{i,t} = f(∆NS^j_{i,t}) + α_i + μ_j + δ_t + ε^j_{i,t}, where:
  - i = country, t = year (2023 and 2024), j = sector (OECD ICIO).
  - α captures country fixed effects; μ industry fixed effects; δ a year dummy.
- Focus on goods sectors; aggregate service industry assigned a subsidy of zero in model simulations.
- Data source for counts: GTA (changes in subsidy counts); data for values: NIPO (used to estimate f(·)).
- Selected predictive coefficient (linear specification): 35.8 on ∆NS (standard error = 9.5).
- Alternative estimate when excluding fixed effects: coefficient = 47.3 (standard error = 12.7) — scales up estimated subsidy value uniformly across countries and sectors.

### Cross-validation and model selection
- Method: 10-fold cross-validation (folds formed by randomly selecting groups of countries; 39 plus the EU per fold).
- Candidate functions for f(·): dummy variables for up to 20 quantiles of ∆NS, linear, and polynomial functions up to fifth order.
- Performance metric: median absolute deviation (MAD) of prediction errors (robust to outliers).
- Result: linear model minimizes both median and average MAD and is selected.

### Data cleaning and alignment with the model
- Restriction to subsidy measures transferring resources directly from governments to firms; categories included in NIPO: “Production subsidies”, “State aid, unspecified", “Capital injection and equity stakes (including bailouts)", “Financial grant", “In-kind grant", and “State aid, nes" (grouping follows UNCTAD(2019) classification).
- Excluded measures: tax breaks (reduce government revenues; actual transfer amounts hard to estimate at introduction) and preferential state loans (transfer risk; not aligned with model assumption of firms without financial constraints).
- For budgeted vs. disbursed amounts: allocate budgeted value proportionally over subsidy duration based on days active within each year.
  - Example: subsidy introduced July 1, 2023 and expiring June 30, 2024 → budget split equally between 2023 and 2024.
  - For measures without specified expiration date (about 80 percent of the sample), impute duration using sample average of about 809 days.
- Product targeting: NIPO specifies HS 6-digit products (2012 revision); to construct subsidy rates for 24 OECD ICIO sectors, aggregate values and counts within each sector and allocate measures spanning multiple sectors proportionally based on sectoral share of targeted HS 6-digit products.
- Note: restricting to direct transfers understates total subsidy support over time because tax reductions and preferential credit have become more important.

### Back-casting methodology and sample construction
- Apply NIPO-estimated linear relationship (coefficient = 35.8 on ∆NS) to full NIPO dataset and to yearly changes in subsidy counts from GTA to predict annual changes in subsidy values from 2009 onward.
- Within GTA: calculate cumulative sum of subsidy measures introduced since 2009 that remain in force in each given year up to 2023.
- Apply same cleaning steps to GTA as for NIPO: restrict to direct transfers, impute durations for measures without expiration dates, distribute multi-sector subsidies proportionally.
- For each sector, count variable equals difference between GTA-classified trade-distortive (“red”) subsidy measures and the (very low) number of trade-liberalizing (“green”) subsidies.
- Focus period for analysis and simulations: start in 2015 to reduce downward bias from missing legacy subsidies introduced before 2009 and because industrial policy activity increased after 2015.
- Sample restriction for simulations: 10 largest subsidizers during 2015-23; other countries grouped as rest-of-the-world (ROW).
- Predicted subsidy values expressed as share of sectoral value added from OECD ICIO tables.
  - OECD ICIO extends through 2022; for 2023 sectoral value added estimated by applying country-level annual GDP growth rates to 2022 sectoral values.

### Estimated subsidy patterns and strategic sectors
- Countries in model simulations: ten largest subsidizers (per 2015-23 estimates) plus ROW.
- China:
  - Average subsidy relative to value added over 2015-23 = 1.8 percent.
  - Subsidies grew from 1 to 2.6 percent of value added over the period.
- United States:
  - Aggregate subsidy rate = 1.3 percent over 2015-23.
- European Union:
  - Aggregate subsidy rate = 0.6 percent over 2015-23.
  - Estimated direct subsidies as share of goods value added in 2023 = 1 percent (comparison point cited).
- Global averages in 2023:
  - Strategic sectors: 1.8 percent of value added.
  - Other sectors: 0.9 percent of value added.
  - In 2015 both strategic and other sectors = 0.5 percent.
- Definition of strategic sectors:
  - Use Advanced Technology Products (ATPs) list from US Census Bureau: 518 HS 10-digit products (HS 2012), grouped into ten categories (biotechnology, life sciences, opto-electronics, information & communications, electronics, flexible manufacturing, advanced materials, aerospace, weapons, and nuclear technology).
  - Match ATP list to GTA product-level data, aggregate to HS 6-digit (consider HS 6-digit an ATP if at least one HS 10-digit subcategory is ATP).
- OECD ICIO sectors containing at least one ATP (eight sectors designated strategic): fabricated metals, other manufacturing, chemicals, pharmaceuticals, electrical equipment, machinery, transport equipment, and electronics.
- Observed patterns:
  - Subsidies directed more toward strategic sectors in most countries; largest differences in China, Canada and Russia.
  - In US and EU, subsidies as share of value added higher in non-strategic sectors.
  - Increased bias toward strategic sectors over 2015-23, with largest increases in China, Australia, India and Canada.
  - Country-level total subsidies over gross output in goods sectors during 2015-23: China = 0.5 percent, US = 0.5 percent, EU = 0.2 percent.
- Sectoral detail (mentioned patterns):
  - In China, three sectors with largest subsidy rate increases: pharmaceuticals, electronics, and electrical equipment — all strategic.
  - In US and EU, large increases observed in non-strategic sectors like agriculture and mineral products.
  - Largest increases in subsidy rates affecting strategic sectors (electronics and electrical equipment) observed in Australia and Canada, starting from values close to zero in 2015.

### Comparisons with other measurement initiatives
- MAGIC database (OECD,2025a) provides comparable cross-country and sectoral focus; both datasets identify China as largest subsidizer.
- MAGIC reported China’s average subsidy rate from grants as percentage of total revenues in sampled firms = 0.5 percent over 2005-22, matching the paper’s average during 2015-23.
- OECD (2025a) reports North America average over 2005-22 for grants as percent of revenues = 0.1 percent; paper’s US 2015-23 average estimated subsidy as percent of gross output = 0.5.
- European Commission State Aid Scoreboard (European Commission,2025) reports 0.6 percent of GDP (including services); paper reports 1 percent of goods value added in 2023.

### Data caveats and limitations
- GTA likely under-counts policy measures in smaller and emerging economies; excluding years before 2015 mitigates but does not eliminate under-counting (example: zero subsidy counts for Saudi Arabia and Argentina in early years of 2015-23).
- Legacy subsidies introduced before 2009 but active during 2015-23 are missing and bias estimates downward.
- Cross-country comparisons complicated by reliance on mixed sources (official government sources and firm financial statements) that can record firm- or region-specific measures separately when they belong to a single policy intervention.
- Estimation hinges on empirical relationship between subsidy values and counts estimated on NIPO data as of February 2025; future data releases may shift this relationship and affect back-casting.
- Restricting to direct transfer instruments (necessary for alignment with model) likely understates overall subsidy values because tax reductions and preferential credit are increasingly important.
- Underestimation of subsidy values for emerging economies may be substantial; alternative evidence suggests “direct funding” can account for around 1.5 percent of GDP in middle income economies (Fernandes and Reed (2026) — noted as context).

*Source: wpiea2026155-source-pdf - 24. Second, we apply these estimates to back-cast subsidy values over 2009-23.*

### 2023. This is slightly lower than our estimates shown in Figure3, panel (b). They also report higher

### wpiea2026155-source-pdf - 2023

### Model framework
- Framework builds on Ju et al. (2024) and extends the multi-country, multi-sector trade model of Caliendo and Parro (2015).
- Structure:
  - N countries and J sectors; workers immobile across countries but mobile across sectors within a country.
  - Representative consumer has Cobb-Douglas across sectors and CES across varieties (equation (2)).
  - Shipping iceberg costs τ^j_in with τ^j_ii = 1 and ad valorem import tariffs t^j_in with t^j_ii = 0.
  - Country i can apply a uniform production subsidy s^j_i across destinations; define ˜t^j_in ≡ 1 + t^j_in and ˜s^j_i ≡ 1 + s^j_i.
  - Variety unit cost c^j_i(ω) = (1 / z^j_i(ω)) c^j_i and sectoral unit cost index given in equation (3).
  - Productivity z^j_i(ω) drawn i.i.d. from a Fréchet with Pr(z^j_i(ω) ≤ z) = exp(−T^j_i z^{−θ^j}), z > 0, θ^j > max{σ^j − 1, 1} (equation (4)).
  - Scale elasticities ψ^j capture external scale economies (sectoral production externalities).

### Equilibrium and gravity relations
- Sectoral price index in destination n:
  - P^j_n = [∑_{i=1}^N T^j_i (c^j_i τ^j_in ˜t^j_in ˜s^j_i)^{−θ^j}]^{−1/θ^j} (equation (5)).
  - Subsidies reduce unit costs and thus put downward pressure on prices.
- Expenditure share of country n on sector j goods from country i:
  - π^j_in = X^j_in / X^j_n = T^j_i (˜s^j_i)^{θ^j} (c^j_i τ^j_in ˜t^j_in)^{−θ^j} (P^j_n)^{−θ^j} = [e^{s^j_i} L^j ψ^j_i]^{θ^j} π^{j,CP}_in (equation (6)).
  - Augmented productivity due to subsidies: T^j_i (˜s^j_i)^{θ^j}.
- Model solved in changes (ˆx ≡ x′ / x); relative changes trade equation (assuming time-invariant T):
  - ˆπ^j_in = [ˆc^j_i ˆτ^j_in ˆ˜t^j_in ˆ˜s^j_i]^{−θ^j} / ∑_{k=1}^N π^j_kn [ˆc^j_k ˆτ^j_kn ˆ˜t^j_kn ˆ˜s^j_k]^{−θ^j} (equation (7)).

### Decomposition of trade effects
- Approximate decomposition of ∆ ln Exp^j_i into six components (equation (8)):
  - Exporter-specific channels (multiplied by θ^j):
    - Subsidy (direct partial equilibrium): θ^j ∆ ln ˜s^j_i.
    - Productivity (scale externalities): θ^j ψ^j ∆ ln L^j_i.
    - Wage effect: −θ^j β^j_i ∆ ln w_i.
    - Input price effect: −θ^j (1 − β^j_i) ∑_s γ^sj_i ∆ ln P^s_i.
  - Destination-specific general equilibrium channels:
    - Competition: ∑_{n≠i} r̄^j_ni θ^j ∆ ln P^j_n.
    - Importer expenditure: ∑_{n≠i} r̄^j_ni ∆ ln X^j_n.
- Key conceptual points:
  - Direct subsidy increases lower purchaser prices and expand demand for the subsidized sector’s exports.
  - Productivity channel operates only when ψ^j > 0 (sectoral external economies) and reflects factor reallocation into subsidized sectors.
  - Wage channel: stronger domestic subsidy scaling raises labor demand and wages, potentially reducing export competitiveness.
  - Input-output channel: subsidies in supplier sectors lower input prices and can boost downstream exports; the reverse occurs if inputs come from non-subsidized sectors contracting.
  - Competition and importer-expenditure channels capture multilateral resistance and foreign demand changes, and can offset direct gains.

### Calibration and simulation design
- Calibration targets:
  - Ten countries with the largest estimated subsidies during 2015-23 and ROW aggregate.
  - 20 sectors: 19 goods sectors plus a services aggregate (aggregation details described in text).
  - Base year for trade flows: OECD ICIO database for 2015.
  - Subsidy shocks calibrated using 2015-23 estimates divided by sectoral gross output kept fixed at its 2015 level.
  - Baseline assumes import tariffs and bilateral trade costs held constant: ˆτ^j_in = ˆ˜t^j_in = 1.
- Elasticities and shares:
  - Sectoral trade elasticities θ^j sourced from Giri, Yi and Yilmazkuday (2021); manufacturing θ^j range from 2.9 to 8.9; median value assigned to agriculture, mining and services.
  - Scale elasticities ψ^j from Bartelme et al. (2025): ψ^j range from 0.06 to 0.22 and set to zero for non-manufacturing sectors.
  - Country-sector expenditure shares α^j_i, value-added shares β^j_i, and input-output shares γ^sj_i calculated from OECD ICIO data.
  - Aggregate trade balances held exogenous at 2015 levels; value-added flows used for initial factor income w_i L^j_i.
- Numerical solution:
  - Model solved in changes using iterative contraction mapping algorithm (Ju et al., 2024) updating ˆw_i, ˆP^j_n, ˆL^j_i, and ˆX^j_n until convergence.
- Data and scenario details:
  - Baseline tariffs from ITC MacMap for 2015.
  - Tariff shock extensions include observed US-China changes during 2018-19 and US/China tariff changes from February 2025 until March 2026 (WTO-IMF Tariff Tracker as of March 2026).
  - Bilateral applied tariffs aggregated to ICIO sectors using import-weighted averages with 2015 import weights from CEPII BACI.

### Key quantitative facts used in simulations
- Sectoral trade elasticities θ^j for manufacturing: range from 2.9 to 8.9.
- Scale elasticities ψ^j: range from 0.06 to 0.22; set to zero for non-manufacturing sectors.
- Model calibrated to the ten largest subsidizers during 2015-23 (EU member states aggregated into single entity).
- Sector aggregation: 20 sectors (19 goods + services aggregate).
- Base year aggregation and trade data: OECD ICIO 2015.
- Baseline shock holding: ˆτ^j_in = ˆ˜t^j_in = 1.
- Example subsidy decomposition note: the 0.6 percent figure is obtained by multiplying the value of state support in 2023 as a share of EU GDP (1.09 percent) by the share of direct grants (59 percent).

### Interpretation and intended use of results
- Simulations are interpreted as long-run responses to industrial policy under free factor reallocation across sectors; results reflect steady-state adjustments likely to materialize years after initial policy changes.
- Analysis focus:
  - How export and import flows adjust in general equilibrium across sectors and countries following 2015-23 subsidy rate changes.
  - Welfare implications from unilateral and global perspectives.
  - Concentration on three largest exporters of strategic products: China, the EU, and the US, while also analyzing combined shocks across the ten economies and ROW.

*Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026155-source-pdf.pdf*

### 4.1  Trade effects of subsidies

### 4.1 Trade effects of subsidies

### Mechanism
- Simulated 2015-23 changes in subsidies reallocate resources toward targeted industries and away from others, raising production and exports in more heavily subsidized sectors and reducing imports in those sectors.
- Economies of scale magnify these effects: targeted sectors with higher scale elasticities experience productivity surges, generating higher production and exports and drawing further resources away from less subsidized sectors.
- Within-economy reallocations produce international spillovers by altering international prices.

### Country-specific trade impacts
- China-only subsidy scenario:
  - Exports in strategic sectors rise by 12 percent.
  - Imports in strategic sectors drop by 8 percent.
  - China’s trade surplus in strategic sectors is 30 percent higher at 0.7 trillion USD in the counterfactual than at baseline.
- EU and US subsidy scenarios:
  - Subsidies increase exports and decrease imports in strategic sectors; opposite trends occur in less-subsidized sectors.
  - Trade effects from EU and US subsidies are smaller than those from China’s subsidies.
- All ten largest subsidizers and ROW implementing 2015-23 changes:
  - Trade effects are qualitatively similar to the China-only scenario, underscoring the dominant role of China’s subsidy responses.

### Cross-border spillovers and third-country effects
- Exports by the EU and the US in strategic sectors decline by around 2 percent following increases in China’s subsidies.
- ROW aggregate (including important exporters in strategic sectors such as Korea) experiences the largest percent contraction in exports in strategic sectors under China-only subsidies.
- Non-subsidizing countries increase their imports by up to 3 percent.
- Exceptions under the all-subsidizer scenario: Australia and Canada register large percent increases in subsidies targeting strategic sectors and correspondingly boost exports in those sectors.

### Global market shares and sectoral trade balances
- China’s share of world exports in strategic sectors rises from 27 percent at baseline to 29 percent under the subsidy counterfactual.
- China’s expansion in strategic sectors is reflected in sectoral trade balances: China’s trade surplus in strategic sectors is 30 percent higher at 0.7 trillion USD in the counterfactual than at baseline, while the US and ROW trade deficits in the same sectors widen.
- Policy shocks have no effect on aggregate trade balances in the model by construction, but sectoral net exports shift substantially.

### Sectoral detail — Electronics and specialization
- China’s overall increase in exports in strategic sectors (even when all countries implement 2015-23 changes) is driven by the electronics industry:
  - China’s electronics exports increase by around 20 percent.
  - China’s share of world electronics exports increases from 39 to 45 percent.
  - China’s net electronics exports surge from 0.2 trillion to approximately 0.3 trillion USD.
- Resources shift away from less-subsidized but significant baseline sectors such as textiles and agriculture.
- Under the all-subsidizer scenario, the EU and the US experience substantial reductions in electronics exports, while Australia, Canada, and India experience the largest percent increases in electronics exports (supported by significant increases in their subsidy rates). The US, Japan, and ROW face the largest declines in electronics exports.

### Mechanisms driving export changes (decomposition)
- Decomposition (equation (8)) highlights that subsidy effects operate through multiple channels: direct price effects, input-output linkages, productivity responses from economies of scale, and competition effects from foreign wage changes.
- China:
  - Reallocation toward electronics yields strong productivity effects due to economies of scale.
  - Productivity gains account for the majority of the rise in China’s electronics exports; firms in electronics exhibit a 5 percent decline in the before-subsidy sectoral producer price.
  - Input-output linkages amplify export growth via lower input prices.
- EU and US:
  - Productivity effects matter most in sectors with the largest relative export changes.
  - Spillovers from China’s export expansion lead to employment declines of 6 percent in the US and 2 percent in the EU in electronics, lowering productivity through economies of scale and decreasing exports.
  - Input-output linkages play a smaller role than in China due to smaller sectoral price index changes and lower shares of intermediates in total production costs (average share of intermediates in total costs: China approximately 75 percent, EU 65 percent, US 58 percent).
  - Competition effect on exports is large and negative due to lower foreign wages and stronger competition abroad.

### Role of economies of scale and robustness checks
- No-scale (ψj = 0 for all sectors) counterfactual:
  - Trade effects of subsidies are weaker than in the baseline model with external economies of scale.
  - Example: under this no-scale setting, the increase in China’s exports in strategic sectors is 5 percent (compared with 12 percent in the baseline), indicating that as much as half of China’s export response can be attributed to induced productivity changes.
- Alternative scale elasticities (Bartelme et al. (2025) baseline without input-output linkages; higher elasticities):
  - Trade effects are qualitatively similar but larger in magnitude.
  - Example: China’s exports in strategic sectors increase by more than 40 percent, while exports in other sectors decline by 30 percent; exports from other countries in those industries fall by more than 10 percent.
- Alternative elasticity calibration (Lashkaripour and Lugovskyy (2023)):
  - Trade effects remain qualitatively similar under this different set of trade and scale elasticities.

### Interaction with recent tariff actions (2015–March 2026)
- Tariff episodes:
  - Major increase in bilateral US-China tariffs occurred in 2018-19 and persisted after 2020; starting February 2025 the US intensified tariff hikes on imports from China and extended increases to all trading partners and most sectors, with China retaliating.
- Import-weighted bilateral US-China tariffs by sector (using 2015 import weights):
  - US average tariffs on imports from China: 3 percent in 2015 → 16 percent after 2018-19 → 31 percent as of March 2026.
  - China’s average tariffs on US imports: 6 percent in 2015 → 27 percent as of March 2026.
  - In China, non-strategic sectors’ import-weighted tariffs on US imports: 8 percent → 34 percent; strategic sectors: 4 percent → 22 percent.
- US tariffs on all trading partners:
  - Average US tariffs were lower for strategic sectors in 2015 but increased to roughly the same level as other sectors at 4.5 percent; reached 16.4 percent as of March 2026, surpassing the average tariffs for other sectors at 13.7 percent.
- Correlation with scale elasticities:
  - US tariff hikes correlate with scale elasticities across sectors (correlation coefficient equal to 0.22), with the notable exception of metals sectors.
  - There is zero correlation between increases in China’s import-weighted average tariffs and scale elasticities across sectors.

*Source: IMF working paper chapter "4.1 Trade effects of subsidies" (content unit: wpiea2026155-source-pdf).*

### Appendix instead shows the changes in sales from China and the US across destination

### wpiea2026155-source-pdf - Appendix instead shows the changes in sales from China and the US across destination markets, under the subsidy-only scenario and the two tariff scenarios

### US-China 2018-19 tariffs: trade and sales by destination
- The US-China tariffs of 2018-19 lower China’s export growth in strategic sectors and deepen the drop in China’s imports in the same sectors relative to a scenario with subsidies only.
- US tariffs on China fail to raise US exports in both strategic and other sectors, while US imports go down.
- The tariffs contain the rise of China’s global market share in strategic sectors, with the decline relative to the only-subsidy scenario mostly picked up by the EU and other countries.
- Dissection by destination market (Figure A.13 in Appendix):
  - Under the subsidy-only scenario, China’s exports to the US in strategic sectors increase by 12 percent.
  - Once the 2018-19 tariffs are included, that 12 percent increase reverses to a 30 percent decline.
  - US exports to China, which fell modestly under the subsidy-only scenario, deepen to roughly a 30 percent drop when 2018-19 tariff changes are accounted for.
- The change in sales in strategic sectors across other destinations is only mildly impacted by the 2018-19 tariffs.
- Trade deflection: The increase in China’s exports toward non-US destinations reflecting trade deflection and the rerouting of supply chains is attenuated by the negative shock in external demand from the US, which limits economies of scale for China’s exporters.

### Tariff actions in 2025 (as of March 2026): compounded effects and destination reallocation
- The 2025 tariff actions compound the impact of the 2018-19 tariff increases.
- Under a scenario with subsidies and US and China’s tariffs as of March 2026:
  - China’s exports in strategic sectors decline by 4 percent.
  - US imports in strategic and other sectors plummet by around 25 percent, while US exports drop relatively less.
- Asymmetry arises from the sectoral structure of US tariffs coupled with economies of scale.
- Effects across destinations:
  - In the US, sales in strategic sectors are redirected toward the domestic market: domestic sales increase by around 13 percent.
  - The decrease in US exports is driven by a drop in sales to China.
  - The 2025 tariff actions lead to a less pronounced (1 pp lower) increase in China’s exports to non-US markets in strategic sectors, due to a negative demand shock from higher US tariffs that dampens China’s resource reallocation toward strategic sectors such as electronics.
- Mechanism: weaker productivity boost from economies of scale in China leads to a smaller expansion in sectoral exports that outweighs any terms-of-trade benefits from US tariffs driving down Chinese wages.

### Efficiency and welfare implications
- In models with economies of scale, subsidies and import tariffs have ambiguous effects on efficiency and welfare.
- Production subsidies proportional to sectoral scale elasticities are first best because they target production externalities; any deviation from optimal subsidy distribution can create misallocation and reduce welfare.
- Unilateral subsidies can create positive terms-of-trade spillovers when targeted sectors have high scale elasticities and low trade elasticities; however, deviations from unilaterally optimal tariff levels can lead to distortions outweighing terms-of-trade gains.
- Simulated impacts (Figure 11):
  - Welfare decreases globally under the subsidies scenario, as fiscal costs of the policies outweigh any efficiency gains.
  - Real wages go up in most countries under the 2015-23 subsidy changes (panel a), because the 2015-23 changes in subsidy rates correlate with scale elasticities.
  - The increase in real wages is stronger for countries implementing larger subsidy increases in strategic sectors (those sectors have higher scale elasticities).
  - Despite higher real wages in many countries, real income (welfare-relevant, includes changes in net government expenditure) decreases globally and for most countries under the subsidies scenarios, indicating observed recent industrial subsidies are far from optimal.
  - Adding recent tariff actions deepens global inefficiencies and creates asymmetric effects across countries:
    - Production and consumption distortions plus negative terms-of-trade externalities on third countries lead to a decrease in average real wages under a scenario including the most recent tariff actions, outweighing any efficiency gains from subsidies.
    - Counterfactual losses in global welfare widen when tariffs are added.
    - US welfare increases slightly under the 2025 tariff scenario because higher tariff revenues more than offset the reduction in real wages, moderated by tariff hikes concentrated in sectors with higher scale elasticities. This result depends on the lack of retaliation against US tariff hikes by all countries except China.
    - Welfare losses deepen for all tariffed countries under the subsidy-and-tariff scenario.
- Robustness and model variants:
  - Without external economies of scale, there are no production externalities and welfare decreases under the subsidy scenario for all countries (Figure A.14 in Appendix).
  - In that no-scale-elasticity variant, the efficiency costs of tariffs for the US are deeper and tariffs are welfare reducing also for the US, confirming results in Rotunno and Ruta (2026).
  - Simulations with higher scale elasticities (Figure A.15) show stronger efficiency gains from subsidies for countries like China and Canada that subsidize more strategic sectors, but globally subsidies remain inefficient and welfare-reducing; adding recent tariff actions deepens global inefficiencies though the US may realize stronger gains by increasing tariffs more in sectors with higher scale elasticities.
  - Using trade and scale elasticities from Lashkaripour and Lugovskyy (2023) (Figure A.16) confirms overall effects on efficiency and welfare.

### Conclusion and avenues for future research
- Main findings:
  - China’s subsidies in strategic sectors, especially electronics, have notable trade impacts through productivity responses.
  - Subsidies by the EU, the US, and other major subsidizers exert relatively smaller trade spillovers.
  - Countries subsidizing less experience export losses in targeted sectors, while some reallocate resources toward sectors where China contracts.
  - The US-China 2018-19 tariffs and the tariff actions in 2025 moderate these dynamics, but both subsidies and tariffs come at the cost of lower welfare globally.
  - Subsidies during 2015-23 are higher in sectors with stronger production externalities, increasing real wages, but fiscal costs and terms-of-trade effects outweigh any efficiency gains.
  - Tariffs deepen efficiency losses by exerting negative externalities on tariffed countries, and a subsidy-tariff spiral amplifies global inefficiencies.
- Suggested future research directions:
  - Explore the role of other industrial policy instruments, such as tax incentives and preferential financing.
  - Incorporate dynamic elements and frictions to capture adjustment costs and transitions to long-run changes.
  - Improve calibration and understanding of scale elasticities, especially for non-manufacturing sectors and services.
  - Model endogenous policy responses by trade partners to better capture interactive adjustments to changing trade flows.

*Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026155-source-pdf.pdf*

### References

### References and Appendix A — Quantitative model and Additional Tables/Figures

### H3 References overview
- Bibliographic compilation of works cited in the chapter, including but not limited to:
  - Aiyar et al.2023; Bartelme et al.2025; Barwick et al.2025; Becko and O’Connor.2024; Bhagwati and Ramaswami.1963; Boullenois et al.2025; Bown.2021, 2024; Caliendo and Parro.2015; Cesa-Bianchi et al.2026; Choi and Levchenko.2025; Clayton, Maggiori, and Schreger.2023–2025; Cuñat and Zymek.2025; Dekle, Eaton, and Kortum.2007; Ethier.1982; European Commission.2025; Evenett et al.2024–2025; Fajgelbaum et al.2024; Fang et al.2025; Fernandes and Reed.2026; Freund et al.2024; Garcia-Macia et al.2025; Giri, Yi, and Yilmazkuday.2021; Goldberg et al.2024; Gourinchas et al.2026; Graham.1923; Grossman and Rossi-Hansberg.2010; Grossman and Sykes.2025; Hirschman.1945; Hodge et al.2024; Huang et al.2025; IMF.2025; Itskhoki and Mukhin.2025; James et al.2013; Juhász et al.2022, 2024; Ju et al.2024, 2026; Kalouptsidi.2018; Krugman.1979; Kucheryavyy et al.2023; Lane.2025; Lashkaripour and Lugovskyy.2023; Lyn and Rodríguez-Clare.2013; Machado Parente et al.2025; Manelici and Pantea.2021; Mattoo et al.2024; Mavroidis.2025; Mearsheimer.2014; Mohr and Trebesch.2025; OECD.2025a–c; Rotunno and Ruta.2024a, 2024b, 2026; Simonovska and Waugh.2014; UNCTAD.2019; WTO-IMF.2026; Zhang.1993.
- References preserve original citation formatting and years as listed.

### H3 Quantitative model — equilibrium characterization (Appendix A.1)
- Sectoral employment equation (A.1):
  - w_i L^j_i = β^j_i ˜s^j_i Σ_{n=1}^N Σ_{j in n} ˜t^j_in
  - Interpretation: subsidies increase labor income in the subsidized sector and country by raising demand for its goods across all countries.
- Labor market clearing (A.2):
  - Σ_{j=1}^J L^j_i = ̄L_i
  - With fixed labor supply ̄L_i and immobile labor across countries, subsidies reallocate workers across sectors within a country to satisfy (A.2).
- Total income (with production subsidy collected before import tariffs) (A.3):
  - Y_i = w_i ̄L_i + R_i + D_i,  R_i ≡ Σ_{j=1}^J Σ_{k=1}^N t^j_ki ˜t^j_ki X^j_ki − Σ_{j=1}^J s^j_i Σ_{n=1}^N 1/˜t^j_in X^j_in
  - Notation identifies R_i as Import Tariff Revenue and the subtraction term as Production Subsidy Expenditure.
- Final consumption price index (Cobb–Douglas across sectors) (A.4):
  - P_n = Π_{j=1}^J (P^j_n)^{α^j_n}
- Sectoral expenditure (A.5):
  - X^j_i = α^j_i Y_i + Σ_{s=1}^J (1−β^s_i) γ^s_j_i Σ_{n=1}^N X^s_in ˜t^s_in
- Equilibrium unknowns and equations:
  - Given parameters {θ^j, ψ^j, α^j_i, β^j_i, γ^s_j_i, ̄L_i, t^j_in, T^j_i, D_i, τ^j_in}, an equilibrium is {w_i, L^j_i, P^j_i, X^j_i} satisfying:
    1. Sectoral price indices P^j_n satisfy equation (5) in main text;
    2. Sectoral employment satisfies (A.1);
    3. Labor market clearing via (A.2);
    4. Sectoral goods markets clear via (A.5).
  - The system comprises 3×N×J + N equations and 3×N×J + N unknowns.

### H3 Model in differences and solution approach
- Counterfactual-to-baseline ratio notation: for any x, ˆx ≡ x′/x.
- Sectoral unit cost (Cobb–Douglas) in differences (A.6):
  - ˆc^j_i = (ˆL^j_i)^{−ψ^j} ˆw_i^{β^j_i} [Π_{s=1}^J (ˆP^s_i)^{γ^s_j_i}]^{1−β^j_i}, with Σ_{s=1}^J γ^s_j_i = 1.
- Cost shifter for shipments i→n in sector j:
  - Z^j_in ≡ (ˆc^j_i ˆτ^j_in ˆ˜t^j_in ˆ˜s^j_i)^{−θ^j}.
- CES price index change (A.7):
  - ˆP^j_n = [Σ_{i=1}^N π^j_in Z^j_in]^{−1/θ^j}, where π^j_in are baseline trade shares.
- Changes in sectoral revenues (A.8):
  - Σ_n b Σ_j in ˜t^j_in = Σ_n ν^j_in ˆπ^j_in ˆX^j_n ˆ˜t^j_in, with ν^j_in ≡ X^j_in/˜t^j_in Σ_m X^j_im/˜t^j_im.
- Employment changes tied to revenue changes (A.9):
  - ˆL^j_i = ˆ˜s^j_i ˆw_i Σ_n ν^j_in ˆπ^j_in ˆX^j_n ˆ˜t^j_in.
- Employment-weighted average constraint with fixed labor supply (A.10):
  - Σ_{j=1}^J λ^j_i ˆL^j_i = 1,  λ^j_i ≡ L^j_i/̄L_i.
- Nominal income changes (A.11):
  - ˆY_i = ζ_{w,i} ˆw_i + ζ_{R,i} ˆR_i + ζ_{D,i} ˆD_i, where ζ_{w,i}, ζ_{R,i}, ζ_{D,i} are baseline shares of labor income, net tariff revenue, and deficits.
- Consumer price index aggregation (A.12):
  - ˆP_n = Π_{j=1}^J (ˆP^j_n)^{α^j_n}.
- Sectoral expenditure in differences (A.13) with definitions ξ^j_n, κ^j_s_n, ν^s_in as provided in text.
- Decomposition of export changes via log differences leading to equation (A.14) and subsequent Törnqvist aggregation to obtain ∆ lnExp^j_i; assumption set: ∆ lnτ^j_in = ∆ ln˜t^j_in = 0 under a subsidy-only scenario.

### H3 Additional tables and figures — selected quantitative highlights (Appendix A.2)
- Table A.1: ATP share and elasticities by sector (selected exact values)
  - Strategic sectors (means and sector entries preserved):
    - Mean (strategic) 3.9 3.7 0.17 0.23 0.27
  - Other sectors (means):
    - Mean (other) 4.9 3.7 0.10 0.15 0.28
  - Mean (all) 4.5 3.7 0.13 0.19 0.27
  - Example sector rows (exact numeric entries preserved):
    - C20 Chemicals: ATP share 0.03, θ_j (BCDR, 2025) 3.75, θ_j (LL, 2023) 3.97, ψ_j (BCDR, 2025) 0.16, ψ_j (BCDR, 2025 robustness) 0.22, ψ_j (LL, 2023) 0.23
    - C26 Electronics: ATP share 0.42, θ_j (BCDR, 2025) 3.27, θ_j (LL, 2023) 1.24, ψ_j (BCDR, 2025) 0.21, ψ_j (BCDR, 2025 robustness) 0.27, ψ_j (LL, 2023) 0.55
    - S Services: ATP share 0.4, θ_j (BCDR, 2025) 3.00, θ_j (LL, 2023) 0.00, ψ_j (BCDR, 2025) 0.00, ψ_j (BCDR, 2025 robustness) 0.00, ψ_j (LL, 2023) 0.00
  - Note: table preserves sector codes and exact numeric values and sources as presented.
- Table A.2: Regressions comparing predicted vs observed subsidy changes in 2023 (exact coefficients)
  - Dependent variable ∆S_GTA; regressor ∆S_NIPO coefficient entries:
    - Model No FEs: 0.594*** (standard error 0.034), Obs 341, R^2 0.48
    - Sector FEs: 0.526*** (0.088), Obs 341, R^2 0.61
    - Country FEs: 0.543*** (0.046), Obs 334, R^2 0.69
    - Sector FEs + Country FEs: 0.407*** (0.057), Obs 334, R^2 0.80
  - Note: both variables in logs; robust standard errors in parentheses; significance: * 10%; ** 5%; *** 1%.
- Table A.3: Counterfactual changes in exports and imports (in percent) — selected entries preserved exactly
  - Strategic sectors, example rows (columns: Subsidizers CHN EU USA ALL; Flow: Exp Imp Exp Imp Exp Imp Exp Imp):
    - AUS: -3.1 1.7 -0.4 0.1 -0.5 0.1 30.4 -3.1
    - CAN: -1.7 0.2 -0.4 0.1 -1.6 0.4 17.0 0.2
    - CHN: 12.0 -7.6 -0.7 0.2 -0.4 0.0 10.0 -7.1
    - USA: -2.4 2.2 -0.6 0.3 2.7 -1.5 -1.3 2.4
  - Note: table reports percent changes in trade flows at producer prices under four subsidy-implementation scenarios: “China”, “EU”, “USA”, and “ALL”.
- Table A.4: Counterfactual changes in exports and imports by strategic sector (percent) — selected exact entries
  - Export changes (Electronics, Transport eq., Machinery, Electrical eq., Chemicals, Pharma, Oth. manuf., Fabricated Metals):
    - CAN: 61.8 8.4 7.5 77.2 7.0 23.6 -3.2 -1.9
    - CHN: 19.0 2.4 5.2 3.2 2.2 8.5 2.6 3.0
    - USA: -7.4 -2.9 0.2 1.8 1.9 3.4 -0.4 -0.2
  - Import changes (same sector order):
    - CHN: -12.1 -1.3 -3.7 -2.2 -0.7 -6.2 -1.0 -1.2
    - USA: 7.2 3.5 0.4 1.1 0.1 -1.5 0.9 0.9
- Figures and robustness checks summarized (figure captions preserved): model-predicted vs observed subsidy changes in 2023; cross-validation of prediction errors (10-fold); global and country-level subsidy rates and scale elasticities (2015 baseline and 2015–23 changes) for World, China, EU, US; predicted subsidies as share of gross output (2015–23 average and changes) for ten countries with largest estimated subsidy values; world markets in electronics and strategic sectors under subsidy and tariff scenarios; simulated changes in exports/imports under alternative elasticity specifications; import-weighted tariff changes including updates through March 2026 for China–US tariffs.
- Scenario definitions preserved:
  - “subsidy-only” scenarios assume ∆ lnτ^j_in = ∆ ln˜t^j_in = 0.
  - Counterfactual tariff scenarios in figures: “subsidies”, “subsidies + 18-19 tariffs”, and “subsidies + 18-19 tariffs + 25 tariffs” reflect successive additions of bilateral US–China import tariff changes up to March 2026.

### H3 Computational and calibration notes
- Equilibrium solved using difference formulation (hat algebra) following Dekle, Eaton and Kortum (2007) and Ju et al. (2024).
- Elasticities and scale parameters used in calibrations sourced explicitly from:
  - Bartelme et al.(2025) (BCDR, 2025) — baseline and robustness values;
  - Lashkaripour and Lugovskyy(2023) (LL, 2023) — alternative elasticities;
  - Giri, Yi and Yilmazkuday(2021) for trade elasticity values in manufacturing sectors.
- Subsidy value estimation and validation:
  - Predicted subsidy values estimated by applying a coefficient of 35.8 to yearly changes in counts of subsidy measures from GTA data and cumulating over time (see Figure A.7 note).
  - Validation regressions reported in Table A.2 show strong positive association between predicted and observed subsidy changes in 2023 (coefficients and R^2 values as reported above).

*Industrial Policy and Trade Tensions in Strategic Sectors — References and Appendix (wpiea2026155-source-pdf - References). Canonical URL: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026155-source-pdf.pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026155-source-pdf.pdf_